Computer Science > Distributed, Parallel, and Cluster Computing

Title:The Energy Complexity of Broadcast

Abstract: Energy is often the most constrained resource in networks of battery-powered
devices, and as devices become smaller, they spend a larger fraction of their
energy on communication (transceiver usage) not computation. As an imperfect
proxy for true energy usage, we define energy complexity to be the number of
time slots a device transmits/listens; idle time and computation are free.
In this paper we investigate the energy complexity of fundamental
communication primitives such as broadcast in multi-hop radio networks. We
consider models with collision detection (CD) and without (No-CD), as well as
both randomized and deterministic algorithms. Some take-away messages from this
work include:
1. The energy complexity of broadcast in a multi-hop network is intimately
connected to the time complexity of leader election in a single-hop (clique)
network. Many existing lower bounds on time complexity immediately transfer to
energy complexity. For example, in the CD and No-CD models, we need
$Ω(\log n)$ and $Ω(\log^2 n)$ energy, respectively.
2. The energy lower bounds above can almost be achieved, given sufficient
($Ω(n)$) time. In the CD and No-CD models we can solve broadcast using
$O(\frac{\log n\log\log n}{\log\log\log n})$ energy and $O(\log^3 n)$ energy,
respectively.
3. The complexity measures of Energy and Time are in conflict, and it is an
open problem whether both can be minimized simultaneously. We give a tradeoff
showing it is possible to be nearly optimal in both measures simultaneously.
For any constant $ε>0$, broadcast can be solved in
$O(D^{1+ε}\log^{O(1/ε)} n)$ time with $O(\log^{O(1/ε)} n)$
energy, where $D$ is the diameter of the network.